One Humble Quants' View on the Credit Crunch

Since I work in the finance industry, I have been asked by a number of people what I thought lead to the "credit crunch". So I'm attempting here to put down some ideas on what I think.

The short story is everyone down the line. So let's line up the usual suspects

1. The people who bought mortgages they couldn't afford.
Now, I don't know if I can go so far and say the education system in the United States is to blame, however reports do show a lower than average numeracy rate. People at some level have to take responsibility for knowing whether or not they can afford something.

But that's a bit glib. We all know the powerful persuasion techniques of salespeople, and especially when charts and numbers are bandied about.

2. The banks that sold the mortgage.
Ie, the salespeople.

These people should have had some responsibility to be open and honest with their clients. Especially about the whole term of the mortgage. These salespeople were showing the teaser rates, but somehow not emphasizing the fact that these rates reset after a couple of months or years. The long term affordability should have been made clear.

In regular circumstances, the banks would not want to enter into mortgages where the probability of default was high, they would likely lose the principal of the mortgage. However, this is no longer the case -- the banks that sell the mortgages do not take on the risk of default.

So... let's ask the question: Who takes on the risk of bad mortgages? That brings us to the next suspect.

3. Fannie Mae, but ultimately the federal government.
The answer is that the banks did not hold the risk of the mortgages, they were able to offload all of the risk of mortgage default to Fannie Mae (the Federal National Mortgage Association -- FNMA). Fannie Mae bought the mortgages from the banks, so the banks made money on creating the mortgage and then selling it immediately to Fannie Mae. If the banks hold no risk, then they are transformed into the business of mortgage creation -- the more mortgages they create the more money they make, and are never exposed to the risk of default. Therefore they have no incentive to tell their clients that they cannot possibly afford that mortgage.

The next suspect please.

4. Ronald Reagan and Alan Greenspan.
The federal government enacted policy to encourage home ownership throughout country. The premise -- which sounds plausible -- is that having some stake in ownership increases participation in the economy. To set this up, they mandated that Fannie Mae relieve the banks for the mortgages they sell. This reduces the amount of risk they have in-house and allow them to go again and sell another mortgage.

Now, even if Fannie may were mandated from above to buy mortgages in order to get more of the populous to be homeowners, surely the would be exposed to the risk of default and would therefore mandate policy downward to the banks to limit their risk.

Next question: How was Fannie Mae offloading the risk of the bad mortgages?

5. Financial alchemists on Wall Street. (NB: Not the quants!)
The people responsible for consolidating all of the mortgages into a single financial product. Here's the rationale: a single mortgage isn't always the best investment. It doesn't promise regular payments at regular intervals -- the mortgage can be paid down early, or it could even default. But packaging a large number of mortgages together, and then selling smaller "tranches" (or slices -- a literal french translation) can make the payments more reliable. This is done by partitioning the tranches such that the "lower tier" ones are populated by the mortgages that default first, and then the "mezzanine" and "senior" tranches are populated by the mortgages that haven't defaulted. Thus, the senior tranches have a longer expected lifetime. One would expect that on average some percentage of the mortgages default and some percentage of the mortgages are prepaid, but these are all relegated to the lower tranches and do not affect the senior tranches. This plausible sounding argument is based somewhat on the "law of large numbers", which roughly states that if a large number of events are considered, then things average out and we have a better handle on their aggregate behaviour.

I called this alchemy because people on Wall street took all these individual mortgages that the populous couldn't afford and packaged them into a financial product that investment banks all over the world were clamouring to buy. Why would they want to buy these types of products? The answer is that they were very highly rated -- they appeared to be good a good quality investment. How did these investments get this appearance? They were rated highly by the ratings agencies. The next suspect.

6. Ratings agencies.
The ratings agencies are autonomous corporations whose purpose is to determine credit-worthiness. Examples include Standards&Poors, Moodys etc. They do this for municipalities, institutions but also for the tranches mentioned above.

The problem leading to the credit crunch was that the investment banks who were structuring these MBSs (Mortgage Backed Securities) and CDOs (Consolidated Debt Obligations) described above had full access to the policies of the ratings agencies, and even in some cases, could meet and discuss with the agencies how to achieve top ratings.

So the investment bankers (aka the alchemists) could figure out exactly how to structure the CDOs in order to achieve the highest rating, regardless of their content.

Now, I'm not actually saying these people were being purposefully deceitful, but they certainly believed the numbers and equations much more than they had any right to do. The reason for this is that ever since 1973, mathematicians and physicists have been employed in Wall street. 1973 was the year that Black Scholes and Merton figured out the "exact" pricing of an option using "fancy mathematics". This ushered in a new era on Wall street -- an arms race -- where each bank hired more and more physicists developing more and more mathematical finance tools. The point is that their return was extraordinary. Wall street got addicted to math.

This culture grew where the math was, well, if not king, then let's just go with indispensable. Hidden within the price of a CDO is some pretty severe assumptions on the default rates and correlations of individual mortgages. The physicists on Wall street decided they could bring their mathematical sophistication to bear on this issue... This brings us to the next suspect.

7. Ok, maybe the quants too.
WIRED magazine recently ran a cover story on The Formula that Ruined Wall Street -- the Guassian Copula (here is a very interesting take on the formula). This formula encapsulates a technique for turning marginal probability distributions into joint probability distributions (here is an interesting take on this relationship). The inventor of this formula knew full all of the assumptions and limitations built into the formula, but it did allow for tractable pricing of very intensely complicated financial products -- mortgage backed securities, exactly those espoused above.

Now I personally don't believe we can fault the discoverer/inventor of the Guassian copula formula David Li. He masterfully solved a difficult problem with an elegant solution, one which clearly had limitations -- limitations that Li both knew about and tried to convey. (See the Quant Manifesto).

I'm going out on a limb here, but I believe that "prepayment" modeling is more akin to actuarial work -- financial mathematics is a different game altogether. Financial mathematics concerns itself with "arbitrage freedom" -- the idea of no-free lunch, two parties can agree on a price because any other price will benefit one side of the deal more than the other -- and has some formal mathematics conditions when this can be true. The idea behind this is "replication", that one can replicate derivative contracts by buying and selling the underlying securities. Anyway, the point is that the current price of a derivative does not depend on past history, only today's prices in the market.

You can't play these formal mathematical games with prepayment modeling, this relies heavily on historical statistics and assumptions about how various factors work together (such as how prepayments move with interest rate movements).

Anyway I digress. The point here is that the quants stopped doing financial mathematics when they started entertaining models like prepayment models. The limitations should have been made more clear, however most likely these models had moderate success in the past and had never been tested in declining real estate market conditions.

Conclusions

So in total, I guess there are a couple of specific policies that come out of this.
1) Strengthen education. Keep the population numerate and literate.
2) Don't let the CMHC give interest only mortgages.
3) Set up a firewall between ratings agencies and banks.
4) (this wasn't really addressed here) Don't allow bank mergers.